Answer:
The number of molecules in the volume is [tex]N_v = 2.27109* 10^{12}[/tex] molecules
Explanation:
From the question we are told that
The pressure of the ultrahigh vacuum is [tex]P = 8.4*10^{-11} torr = 8.4*10^{-11} * 133 = 1.1172 *10^{-8}Pa[/tex]
The molecular diameter of the gas molecules [tex]d = 2.2*10^{-10} m[/tex]
The temperature is [tex]T = 310 \ K[/tex]
Avogadro's number is [tex]N = 6.02214 *10^{23}\ l/mol[/tex]
The volume of the gas is [tex]V = 0.87 m^3[/tex]
From the ideal gas law[[tex]PV = nRT[/tex]] that the number of mole is mathematically represented as
[tex]n = \frac{PV}{RT}[/tex]
Where R is the gas constant with a value [tex]R = 8.314\ J/mol[/tex]
Substituting values
[tex]n = \frac{1.1172 *10^{-8} * 0.87}{8.314 * 310}[/tex]
[tex]n = 3.771*10^{-12} \ mole[/tex]
The number of molecules is mathematically represented as
[tex]N_v = n * N[/tex]
Substituting values
[tex]N_v = 3.771*10^{-12} * 6.02214 *10^{23}[/tex]
[tex]N_v = 2.27109* 10^{12}[/tex] molecules
